Explanation Given Information: The values of f ( x ) for different values x : f ( − 1 ) = 5 , f ( 1 ) = 3 , f ( 2 ) = 5 Calculation: To obtain the quadratic function at first we will find the coefficients a, b, c . Since, f ( x ) = a x 2 + b x + c . So, f ( − 1 ) = 5 gives, f ( − 1 ) = a ( − 1 ) 2 + b ( − 1 ) + c 5 = a − b + c a − b + c = 5 (I) f ( 1 ) = 3 gives, f ( 1 ) = a ( 1 ) 2 + b ( 1 ) + c 3 = a + b + c a + b + c = 3 (II) f ( 2 ) = 5 gives, f ( 2 ) = a ( 2 ) 2 + b ( 2 ) + c 5 = 4 a + 2 b + c 4 a + 2 b + c = 5 (III) Equations (I), (II) and (III) give, a − b + c = 5 a + b + c = 3 4 a + 2 b + c = 5 Use the Gauss elimination method to obtain the solution of the above system of equation. The matrix corresponding to the system of equation is as follows: [ 1 − 1 1 5 1 1 1 3 4 2 1 5 ] The matrix will be converted into the echelon form by using the elementary row transformation

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ISBN: 9780134469140

Author: Robert F. Blitzer

Publisher: PEARSON

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Chapter 8.1, Problem 40PE

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To calculate: The quadratic function f(x)=ax2+bx+c where f(−1)=5,f(1)=3,f(2)=5.

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Chapter 8.1, Problem 39PE

Chapter 8.1, Problem 41PE

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Chapter 8 Solutions

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The quadratic function f ( x ) = a x 2 + b x + c where f ( − 1 ) = 5 , f ( 1 ) = 3 , f ( 2 ) = 5 .

Solution Summary: The author explains how to calculate the quadratic function f(x) = ax 2+bx+c.

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To calculate: The quadratic function f(x)=ax2+bx+c where f(−1)=5,f(1)=3,f(2)=5.

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Chapter 8 Solutions